Funny. Maarten sees this definition as "obvious", and I do understand
why.
I was brought up an old-fashioned way with lots of correlation before
regression and still tend to see the definition of R-square as the
square of the correlation between observed and fitted as the "obvious"
one.
No doubt there are now people who see a definition in terms of
likelihood results as the "obvious" one.

Continuing this sidelight - I give several formulas for OLS and their
logical Pseudo R^2 analogs at

For OLS, the formulas all give the same results, but the Pseudo R^2
stats all give different numbers. Counter to the claims of some, I
don't think logic alone clearly favors one Pseudo R^2 measure over another.

One thing I do find kind of remarkable is that the Maximum Likelihood
R^2 (aka Cox-Snell) isn't just a logical analog - it is the exact
same formula for OLS R^2 and Pseudo R^2. That might be why, as Nick
says, some may think this is the "obvious" measure.

I'm not quite sure why McFadden's Pseudo R^2 came to be blessed by
Stata, but I suppose it is as good as any.